Integer factorization, etc.
in [Math]
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From: quasi on 17 Apr 2008 18:54 On Thu, 17 Apr 2008 18:50:03 -0400, quasi <quasi(a)null.set> wrote: >On Fri, 18 Apr 2008 03:43:45 -0700 (PDT), Risto Lankinen ><rlankine(a)gmail.com> wrote: > >>On 18 huhti, 05:14, fortune.br...(a)gmail.com wrote: >> >>> I could go on, dude. >> >>Gotcha. I figure it's still OK for me to ask questions. >> >>Question to math experts: >> >>There's an infinite array A of integers. Most elements >>of the array are zero, but a finite subset have some >>other positive value. All elements obey the following >>constraint: >> >>FLOOR(A[n]/2) = SUM(i=1..inf,(A[n-1] MOD 2)*(A[n+1] MOD 2)) > >Something's wrong with the RHS. > >The index variable i doesn't get used. > >Presumably, the i'th summand should depend on both i and n. Or perhaps the summands depend only on i, but the range for the index variable i depends on n. quasi
From: bitsplit on 18 Apr 2008 09:32 On Apr 9, 3:35 pm, Risto Lankinen <rlank...(a)gmail.com> wrote: > On 9 huhti, 21:33, Pubkeybreaker <pubkeybrea...(a)aol.com> wrote: > > > > > On Apr 9, 1:15 pm, Risto Lankinen <rlank...(a)gmail.com> wrote: > > > > On 9 huhti, 20:08, Pubkeybreaker <pubkeybrea...(a)aol.com> wrote: > > > > > > Could you please tell me _WHY_ you think my approach is > > > > > a dead end? Based on your own claim, you never dug into > > > > > the code I sent. > > > > > (1) Presenting code only serves to obfuscate the underlying method. > > > > If you want to present an algorithm then do so. > > > > Please advice about _HOW_. I've already tried my best. > > > Yes. Which is why I presented the analogy with medicine. > > It is pointless for someone without the requisite knowledge > > to try to invent a new surgical procedure. Your reply here > > shows that you lack the basic knowledge to do what you are > > trying to do. > > Ad hominem usually indicates lack of material arguments. > > But hey, I'm not doing this for you, sir. You've taught me > a lot. Not about math, but about math community! I will > continue enjoying the ride on the passenger seat, where > it is possible to observe the landscape. But you, sir, on > the driver's seat, please keep your eyes on the road. > > - Risto - I think Risto shows the youth and enthusiasm that could turn into good progress. But, like me, he needs to learn a whole lot of math before he can start doing the "good stuff". If someone had told me in youth how much I would love math, I would have paid more attention in class. Don't be discouraged Risto. Just pay attention, read, practice, read more, practice more, and have a conscious humility. I don't know much about math, but I think you are not a crank, just mathematically naive. You truly do believe you have something new (or believed at least). It's fun to read some of the stuff on here. Been lurking for a long time. If only the spam, the cranks, and the attention deprived didn't ruin it so... - Carlos
From: Risto Lankinen on 18 Apr 2008 12:27 On 18 huhti, 01:50, quasi <qu...(a)null.set> wrote: > On Fri, 18 Apr 2008 03:43:45 -0700 (PDT), Risto Lankinen > > >There's an infinite array A of integers. Most elements > >of the array are zero, but a finite subset have some > >other positive value. All elements obey the following > >constraint: > > >FLOOR(A[n]/2) = SUM(i=1..inf,(A[n-1] MOD 2)*(A[n+1] MOD 2)) > Something's wrong with the RHS. Typo: 1 -> i (corrected below). FLOOR(A[n]/2) = SUM(i=1..inf,(A[n-i] MOD 2)*(A[n+i] MOD 2)) Thanks for noticing. - Risto -
From: Risto Lankinen on 18 Apr 2008 13:05 On 18 huhti, 12:46, Tim Little <t...(a)soprano.little-possums.net> wrote: > On 2008-04-18, Risto Lankinen <rlank...(a)gmail.com> wrote: > > > This is paradoxical, because square root is easy and factoring hard, > > whilst relaxing constraints should make the task easier. > > Factoring is very easy. It's just slow, for numbers that are very > large. I'm not surprised that relaxing a constraint could turn a slow > square-root finding method into a slow factoring method. How can speed be a factor, if no algorithm was presented. - Risto -
From: bitsplit on 18 Apr 2008 14:55
On Apr 18, 1:05 pm, Risto Lankinen <rlank...(a)gmail.com> wrote: > On 18 huhti, 12:46, Tim Little <t...(a)soprano.little-possums.net> > wrote: > > > On 2008-04-18, Risto Lankinen <rlank...(a)gmail.com> wrote: > > > > This is paradoxical, because square root is easy and factoring hard, > > > whilst relaxing constraints should make the task easier. > > > Factoring is very easy. It's just slow, for numbers that are very > > large. I'm not surprised that relaxing a constraint could turn a slow > > square-root finding method into a slow factoring method. > > How can speed be a factor, if no algorithm was presented. > > - Risto - I can't be sure, but I believe it assumes all known algorithms, for which a complexity analysis has been performed. I believe the best factoring algorithms are exponential time. Usually exponential time algorithms are classified as slow, while polynomial and better are considered "manageale" to fast. The only known and published algorithm known to be polynomial is Shor's algorithm for quantum computers. I don't think there's any quantum computers lying around that can do Shor's for 100+ digit numbers. Hence, factoring is slow. - Carlos |